Surface area and volume of a cube examples :
Here we are going to see some examples problems on finding surface area and volume of a cube.
Example 1 :
The volume of the cube is 125 dm3. Find its side.
Volume of cube = 125 dm3
a3 = 125
a3 = 53
a = 5 dm
Hence side length of cube is 5 dm.
Example 2 :
A container is in the shape of a cube of side 20 cm. How much sugar can it hold?
In order to find the quantity of sugar that the container can hold, we have to find the volume of container.
Side length of cubical container = 20 cm
Volume of container = a3
= 8000 cm3
Example 3 :
A cubical tank can hold 64,000 litres of water. Find the length of the side of the tank.
Let a be the side of the cubical tank. Volume of the tank is 27,000 litres. So,
V = a3 = (27000/1000)
a3 = 27
a = ∛27
a = 3 m
Example 4 :
Three metallic cubes of side 3 cm, 4 cm and 5 cm respectively are melted and are recast into a single cube. Find the total surface area of the new cube.
Side length of 1st cube = 3 cm
Side length of 2nd cube = 4 cm
Side length of 3rd cube = 5 cm
Volume of 1st, 2nd and 3rd cube = 33 + 43 + 53
= 27 + 64 + 125
a3 = 216
a3 = 63
a = 6 cm
Total surface area of new cube = 6a2
= 216 cm2
Hence total surface area of new cube 216 cm2
Example 5 :
Find the L.S.A, T.S.A and volume of a cube of side 5 cm.
Lateral surface area (L.S.A) = 4a2
= 4(52 ) = 100 sq. cm
Total surface area (T.S.A) = 6a2
= 6 (52 )
= 150 sq. cm
Volume of cube = a3
= 125 cm3
Example 6 :
Find the length of the side of a cube whose total surface area is 216 square cm.
Let a be the side of the cube.
Given that T.S.A = 216 sq. cm
6a2 = 216
a2 = 216/6
a2 = 36
a = √36
a = 6 cm
Example 7 :
A cube has a total surface area of 384 sq. cm. Find its volume.
Let a be the side of the cube. Given that T.S.A = 384 sq. cm
6a2 = 384
a2 = 384/6
a2 = 64
a = √64 = 8 cm
Hence, volume = a3 = 83 = 512 cm3
Example 8 :
If the lateral surface area of a cube is 900 cm2, find the length of its side.
Lateral surface area of cube = 4a2
4a2 = 900
a2 = 900/4
a2 = 225
a = √225
a = 15 cm
Hence the side of cube is 15 cm.
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